Question

Consider a four-year bond with a 10 percent coupon paid semiannually (or 5 percent paid every 6 months) and an 8 percent rate of return (rb). Suppose that the rate of return increases by 10 basis points (1/10 of 1 percent) from 8 to 8.10 percent. Then, using the semiannual compounding version of the duration model shown above, how much is the percentage change in the bond's price?

Answer 1

Statement showing price of bond:      (assume face value to be $1000, in case of semiannual years to maturity will be 8 years, coupon payment= 1000*0.05=$50, yield is 4%)
Particulars	Time	PVf @4%	Amount	PV
Cash Flows (Interest)	1.00	0.9615	50.00	48.08
Cash Flows (Interest)	2.00	0.9246	50.00	46.23
Cash Flows (Interest)	3.00	0.8890	50.00	44.45
Cash Flows (Interest)	4.00	0.8548	50.00	42.74
Cash Flows (Interest)	5.00	0.8219	50.00	41.10
Cash Flows (Interest)	6.00	0.7903	50.00	39.52
Cash Flows (Interest)	7.00	0.7599	50.00	38.00
Cash Flows (Interest)	8.00	0.7307	50.00	36.53
Cash flows (Maturity Amount)	8.00	0.7307	1,000.00	730.70
Current Bond Price				1,067.34
Price of bond= $1067.34
Statement showing price of bond:      (assume face value to be $1000, in case of semiannual years to maturity will be 8 years, coupon payment= 1000*0.05=$50, yield is 4.05%)
Particulars	Time	PVf @4.05%	Amount	PV
Cash Flows (Interest)	1.00	0.9611	50.00	48.05
Cash Flows (Interest)	2.00	0.9237	50.00	46.18
Cash Flows (Interest)	3.00	0.8877	50.00	44.39
Cash Flows (Interest)	4.00	0.8532	50.00	42.66
Cash Flows (Interest)	5.00	0.8200	50.00	41.00
Cash Flows (Interest)	6.00	0.7880	50.00	39.40
Cash Flows (Interest)	7.00	0.7574	50.00	37.87
Cash Flows (Interest)	8.00	0.7279	50.00	36.39
Cash flows (Maturity Amount)	8.00	0.7279	1,000.00	727.90
Current Bond Price				1,063.84
Price of bond= $1063.84
Percentage change in bond price=(1063.84-1067.34)/1067.34*100= -0.33%